Question: Solve for $x$ and $y$ using elimination. ${-2x-2y = -24}$ ${3x+2y = 32}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2y$ and $2y$ cancel out. ${x = 8}$ Now that you know ${x = 8}$ , plug it back into $\thinspace {-2x-2y = -24}\thinspace$ to find $y$ ${-2}{(8)}{ - 2y = -24}$ $-16-2y = -24$ $-16{+16} - 2y = -24{+16}$ $-2y = -8$ $\dfrac{-2y}{{-2}} = \dfrac{-8}{{-2}}$ ${y = 4}$ You can also plug ${x = 8}$ into $\thinspace {3x+2y = 32}\thinspace$ and get the same answer for $y$ : ${3}{(8)}{ + 2y = 32}$ ${y = 4}$